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A CYCLIC AND SIMULTANEOUS ITERATIVE ALGORITHM FOR THE MULTIPLE SPLIT COMMON FIXED POINT PROBLEM OF DEMICONTRACTIVE MAPPINGS
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 Title & Authors
A CYCLIC AND SIMULTANEOUS ITERATIVE ALGORITHM FOR THE MULTIPLE SPLIT COMMON FIXED POINT PROBLEM OF DEMICONTRACTIVE MAPPINGS
Tang, Yu-Chao; Peng, Ji-Gen; Liu, Li-Wei;
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 Abstract
The purpose of this paper is to address the multiple split common fixed point problem. We present two different methods to approximate a solution of the problem. One is cyclic iteration method; the other is simultaneous iteration method. Under appropriate assumptions on the operators and iterative parameters, we prove both the proposed algorithms converge to the solution of the multiple split common fixed point problem. Our results generalize and improve some known results in the literatures.
 Keywords
demicontractive mappings;cyclic;simultaneous;split common fixed point;
 Language
English
 Cited by
 References
1.
H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasi-bility problems, SIAM Rev. 38 (1996), no. 3, 367-426. crossref(new window)

2.
H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for Fejer-monotone methods in Hilbert spaces, Math. Oper. Res. 26 (2001), no. 2, 248-264. crossref(new window)

3.
H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.

4.
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems 18 (2002), no. 2, 441-453. crossref(new window)

5.
Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms 8 (1994), no. 2-4, 221-239. crossref(new window)

6.
Y. Censor, T. Elfving, N. Kopf, and T. Bortfeld, The multiple-sets split feasibility prob-lem and its applications for inverse problems, Inverse Problems 21 (2005), no. 6, 2071-2084. crossref(new window)

7.
Y. Censor, A. Motova, and A. Segal, Perturbed projections and subgradient projections for the multiple-sets split feasibility problem, J. Math. Anal. Appl. 327 (2007), no. 2, 1244-1256. crossref(new window)

8.
Y. Censor and A. Segal, The split common fixed point problem for directed operators, J. Convex Anal. 16 (2009), no. 2, 587-600.

9.
A. Moudafi, The split common fixed point problem for demicontractive mappings, Inverse Problems 26 (2010), no. 5, 055007, 6 pp.

10.
A. Moudafi, A note on the split common fixed-point problem for quasi-nonexpansive operators, Nonlinear Anal. 74 (2011), no. 12, 4083-4087. crossref(new window)

11.
B. Qu and N. Xiu, A note on the CQ algorithm for the split feasibility problem, Inverse Problems 21 (2005), no. 5, 1655-1665. crossref(new window)

12.
Y. C. Tang, J. G. Peng, and L. W. Liu, A cyclic algorithm for the split common fixed point problem of demicontractive mappings in Hilbert spaces, Math. Modell. Anal. 17 (2012), no. 4, 457-466. crossref(new window)

13.
F. Wang and H. K. Xu, Approximating curve and strong convergence of the CQ Algo-rithm for the split feasibility problem, J. Inequal. Appl. 2010 (2010), Article ID 102085, 13 pages.

14.
F. Wang and H. K. Xu, Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal. 74 (2011), no. 12, 4105-4111. crossref(new window)

15.
Z. W. Wang, Q. Z. Yang, and Y. N. Yang, The relaxed inexact projection methods for the split feasibility problem, Appl. Math. Comput. 217 (2011), no. 12, 5347-359. crossref(new window)

16.
H. K. Xu, A variable Krasnoselskii-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems 22 (2006), no. 6, 2021-2034. crossref(new window)

17.
H. K. Xu, Iterative methods for the split feasibility problem in infinite dimensional Hilbert spaces, Inverse Problems 26 (2010), no. 10, 105018, 17 pp.

18.
Q. Yang, The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems 20 (2004), no. 4, 1261-1266. crossref(new window)

19.
Q. Yang and J. Zhao, Generalized KM theorems and their applications, Inverse Problems 22 (2006), no. 3, 833-844. crossref(new window)

20.
H. Y. Zhang and Y. J. Wang, A new CQ method for solving split feasibility problem, Front. Math. China 5 (2010), no. 1, 37-46. crossref(new window)

21.
J. Zhao and Q. Yang, Several solution methods for the split feasibility problem, Inverse Problems 21 (2005), no. 5, 1791-1799. crossref(new window)